**Physical Quantities:**

- In physical science, we commonly deal with quantities such as pressure, volume, mass, temperature, current, etc. These quantities are known as physical quantities.

- A physical quantity has two components, namely,

**and its**

__numerical value__**and is written as,**

__unit__Physical quantity | Numerical value | unit |

- Here Physical quantity

**Newton**and its numerical value

**5**

C.G.S Units |

S.I Units |

Physical quantity | Dimension |

Length | L |

Mass | M |

Time | T |

**Definition of Base Physical Quantities:**

__Metre:__

__Metre:__

- The metre is the length of path traveled by light in vacuum during a time interval 1/299 792 458 of a second.

__Unit and dimension of Area:__

- Area = Length × Length
Thus the unit of Area = Unit of Length × Unit of Length

- Unit of Area in

**C.G.S.**System = cm × cm

*= cm²*- Unit of Area in

**S.I**. System is = m × m

**= m²**- Dimension of Area = L × L

*= [L]²*__Unit and dimension of Volume:__

- Volume (V) = Length × Length × Length.
Thus the unit of Volume = Length × Length × Length.

- Unit of Area in

**C.G.S.**System = cm × cm × cm

*= cm³*- Unit of Area in

**S.I.**System is = m × m × m

*= m³*- Dimension of Area = L × L × L

*= [L³]**Unit and dimension of Density:*

- From the definition of Density (d) = Mass/Volume
Thus the unit of density = Unit of Mass/Unit of Volume.

- Unit of Area in

**C.G.S.**System = gm/cm³

*= gm cm⁻³*- Unit of Area in

**S.I.**System is = Kg/m³

*= Kg m⁻³*- Dimension of Area = [M]/[L³]

*= [M L⁻³]*__Unit and dimension of Force:__

- From the Newton Second Low of Motion,
Force = Mass × Acceleration
or, Force = Mass × Velocity/Time
or, Force = Mass × (Length/Time) /Time

- Here Velocity = Length/Time

**∴ Force = Mass × (Length/Time²)**

- Thus the unit of Force in C.G.S. System,
=Unit of Mass × (Unit of Length/Unit of Time²)

- = gm × cm/sec²
= gm cm/sec²
or, gm cm sec⁻²

*or, Dyne*- Again in the same way Unit of Force in S.I System,
= Kg m/sec²
or, Kg m sec⁻²

*or, Newton*- From the above discussion dimension of Force, = dimension of Mass × dimension of Length/dimension of Time².

- Thus the dimension of Force =

*[M L T⁻²]*

__Convert 1 newton into dyne:__**= Kg m/sec² = (1 Kg× 1 m )/(1 sec)²**

*1 Newton*- We know that, 1 Kg = 10³ gm and 1 m = 10² cm

- Thus, 1 Newton = (10³gm × 10² cm)/(1 sec)²
= 10⁵ gm cm/sec2

*= 10⁵ Dyne*__Unit and dimension of Work:__

- From the definition of Work (W) = Force(F) × Displacement(d).
Thus, the unit Work = unit of Force × unit of Displacement(d)

- ∴ Unit of Work in C.G.S. System, = (gm cm/sec²) × cm
or, gm cm²/sec²
or, gm cm²sec⁻²

*or, erg*- And unit of work in S.I. system = (Kg m/sec²) × m
or, Kg m²/sec²
or, Kg m²sec⁻²

*or, Joule*- From the above discussion dimension of Work, = (dimension of Mass × dimension of Length)²)/(dimension of Time²)

- Thus dimension of Work =

*[ML²T⁻²]*

__Convert 1 Joule into erg:__**= 1 Kg m²/sec² = (1 Kg × 1 m² )/1 sec²**

*1 Joule*- We know that, 1 Kg = 10³ gm and 1 m = 10² cm

- Thus, 1 Joule = {10³ gm × (10²)² cm}/1 sec²
= 10⁷ gram cm²/sec²

*=*

**10⁷ erg***Unit and dimension of Force:*

- The ability to doing work is termed as Energy. Thus, the unit and dimension of energy and work is same.

- Unit of Energy in

**C.G.S**System is

**and**

*erg***S.I.**System is

*Joule**Unit and dimension of Pressure:*

- From the definition of Pressure (P) = Force/Area
Thus the unit of Pressure = Unit of force/Unit of area.

- Unit of Pressure in

**C.G.S.**System = erg/cm²

*= erg cm⁻²*- Unit of Pressure in

**S.I.**System is = joule/m²

*= joule m⁻²*- Dimension of Pressure

*= [M L⁻²]*